Problem: What's the first wrong statement in the proof below that $ \triangle ABC \cong \triangle EBC$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. A B C D E F Givens $ \angle BAC \cong \angle CEF$ $, \ $ $ \angle ABC \cong \angle CFE$ $, \ $ $ \overline{BC} \cong \overline{CF}$ $, \ $ $ \angle ABC \cong \angle DBE$ $, \ $ $ \angle ACB \cong \angle BDE$ $, \ $ and $\ $ $ \overline{AC} \cong \overline{DE}$ Proof $ \triangle EBD \cong \triangle ABC$ because AAS $ \overline{BE} \cong \overline{AB}$ because corresponding parts of congruent triangles are congruent $ \triangle EFC \cong \triangle ABC$ because AAS $ \overline{CE} \cong \overline{AC}$ because corresponding parts of congruent triangles are congruent $ \triangle EBC \cong \triangle ABC$ because SSS
Answer: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. There is no wrong statement in this proof.